Primality proof for n = 288467:
Take b = 2.
b^(n-1) mod n = 1.
6271 is prime. b^((n-1)/6271)-1 mod n = 61076, which is a unit, inverse 100323.
(6271) divides n-1.
(6271)^2 > n.
n is prime by Pocklington's theorem.